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Fast Approximation Methods for Fitting Surfaces to Unorganized Point Clouds

AUTHORS

Karl-Heinz Brakhage

ABSTRACT

We present and analyze a novel fast method for scattered data approximation with curves / surfaces which have a representation as a linear combination of smooth basis functions associated with the control points. Our technique can be applied to standard Bezier and B-spline curves / surfaces as well as for subdivision schemes. The approach can be formulated in such way that for the iteration we have a standard least squares problem in each step. A regularization term that expresses the fairness of the intermediate and / or final result can be added. Adaptivity is easily integrated in our concept. Furthermore our approach is well suited for reparameterization occurring in grid generation.